Optical design programs are used to design, model, display, and fabricate imaging systems. Typically, the geometry of the optical surfaces of the imaging system lenses, mirrors, and other components are modeled using polynomial based solutions. See published U.S. Patent Application No. 2009/0228251 incorporated herein by this reference. The resulting resolution of the imaging system, however, may not be sufficient for advanced technologies (e.g., telescopes and the like).
Non-uniform rational basis splines (NURBS) may be used to generate a better mathematical model of a surface. The surface is divided up into rectangular grid sub-areas defined by the grid control points. But, known attempts to optimize NURBS surfaces for optical design programs have not been wholly successful. See also published U.S. Patent Application No. 2009/0228251 and U.S. Pat. No. 8,310,481 both incorporated herein by this reference.